Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory

Yongping Deng, Hidayat Ullah, Muhammad Adil Khan, Sajid Iqbal, Shanhe Wu and Georgios Psarrakos

Journal of Mathematics, 2021, vol. 2021, 1-12

Abstract: In this study, we present some new refinements of the Jensen inequality with the help of majorization results. We use the concept of convexity along with the theory of majorization and obtain refinements of the Jensen inequality. Moreover, as consequences of the refined Jensen inequality, we derive some bounds for power means and quasiarithmetic means. Furthermore, as applications of the refined Jensen inequality, we give some bounds for divergences, Shannon entropy, and various distances associated with probability distributions.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1951799

DOI: 10.1155/2021/1951799

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